Finite Group Databasebeta

← #25072896

Subgroups — #25072896

Order 11008.

918 conjugacy classes of subgroups; only the 171 normal subgroups are shown.

normal subgroups only

This group has 918 conjugacy classes of subgroups — too many to draw. Only its 171 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583629C211yesmaximal, characteristic
2#19144721C212yesmaximal
3#19133813C218yesmaximal, complemented
4#19133321C211yesmaximal, characteristic
5#19133043C212yesmaximal
6C43×#3139C211yesmaximal, characteristic
7#14583629—24no—
8#14583629—22no—
9#14583629C2214yes—
10C2×#13063324—22no—
11C2×#13063323—22no—
12C2×C4×Dic86C2212yes—
13C2×#13063290—22no—
14#14583227—22no—
15#14583181C2214yes—
16#14583106C2214yes—
17#14583054—22no—
18#14583004—24no—
19#14582956C2212yes—
20#14582648C2214yes—
21#14582631C2218yes—
22C43×#533C2211yescharacteristic
23C2×C4⋊Q8×C43C2211yescharacteristic
24C43×#491—22no—
25C43×#487C2214yes—
26C43×#419—22no—
27C4×M16×C43C2211yescharacteristic
28C22×Dic86—22no—
29C22×Dic86D412yes—
30C2×#10621885—24no—
31#13063324—28no—
32#13063324—28no—
33#13063323—28no—
34#13063323—28no—
35C4×Dic86—22no—
36C4×Dic86—22no—
37C4×Dic86D414yes—
38C4×Dic86C2314yes—
39#13063290—28no—
40#13063290—28no—
41C2×C4⋊Dic43D412yes—
42C2×Dic43⋊C4—24no—
43C2×Dic43⋊C4—22no—
44C2×C4×Dic43—22no—
45C2×C4×Dic43—22no—
46#13063256—24no—
47C4⋊(C43⋊C8)C2314yes—
48#13063249—24no—
49#13063248—24no—
50C22⋊(C43⋊C8)—22no—
51#13063236—22no—
52C22×Q8×C43D412yes—
53C2×M16×C43—21no—
54C4⋊Q8×C43—22no—
55C4⋊Q8×C43D412yes—
56C4⋊Q8×C43C2312yes—
57C4⋊Q8×C43C2312yes—
58#125×C43—21no—
59C22⋊Q8×C43—22no—
60C4×Q8×C43—22no—
61#117×C43—21no—
62C2×C4⋊C4×C43—22no—
63C2×C42×C43C2311yescharacteristic
64#103×C43—28no—
65#97×C43—21no—
66C4×C8×C43C2312yes—
67C2×Q8×C43—22no—
68C2×Q8×C43—22no—
69C2×Q8×C43—44no—
70C2×Q8×C43C2×D414yes—
71C22×C4×C43—22no—
72C22×C4×C43C2×D412yes—
73C22×C4×C43C2×D411yescharacteristic
74C22×Dic43—22no—
75C22×Dic43—22no—
76C2×Dic86—22no—
77C2×Dic86—28no—
78C2×Dic86—28no—
79C2×Dic86—84no—
80C2×Dic86C2×D414yes—
81M16×C43—42no—
82C2×C8×C43—22no—
83C4⋊C4×C43—24no—
84C4⋊C4×C43—24no—
85C4⋊C4×C43—22no—
86C4⋊C4×C43—22no—
87C4⋊C4×C43—42no—
88C22⋊C4×C43—41no—
89C42×C43—41no—
90C42×C43C2×D412yes—
91C42×C43C2×D411yescharacteristic
92C42×C43C2411yescharacteristic
93#10621885—48no—
94C4⋊Dic43—22no—
95C4⋊Dic43C2×D414yes—
96Dic43⋊C4—216no—
97Dic43⋊C4—24no—
98Dic43⋊C4—24no—
99C4×Dic43—28no—
100C4×Dic43—24no—
101C4×Dic43—24no—
102C2×C43⋊C8—24no—
103C23×C43#12011yescharacteristic
104Q8×C43—44no—
105Q8×C43—44no—
106Q8×C43—82no—
107C2×C4×C43—22no—
108C2×C4×C43—24no—
109C2×C4×C43—24no—
110C2×C4×C43—44no—
111C2×C4×C43—42no—
112C2×C4×C43#12012yes—
113C2×C4×C43#12011yescharacteristic
114C2×C4×C43C22×D412yes—
115C2×C4×C43C22×D411yescharacteristic
116C2×Dic43—28no—
117C2×Dic43—24no—
118C2×Dic43—24no—
119C2×Dic43—44no—
120Dic86—28no—
121Dic86—24no—
122Dic86—88no—
123Dic86#13718yes—
124C8×C43—42no—
125C43⋊C8—44no—
126#18551—431nomaximal, Sylow
127C22×C43—22no—
128C22×C43#45512yes—
129C22×C43C2×#12011yescharacteristic
130C4×C43—22no—
131C4×C43—21no—
132C4×C43—21no—
133C4×C43—44no—
134C4×C43—82no—
135C4×C43C2×#13714yes—
136Dic43—28no—
137Dic43—44no—
138C2×Q82—431no—
139#3139D4311yescharacteristic
140#3113—432no—
141#1645—438no—
142#1558—431no—
143#1491—432no—
144C2×C43—22no—
145C2×C43#300412yes—
146C2×C43C2×#45511yescharacteristic
147Q82—434no—
148Q82—864no—
149Q82—862no—
150#533C2×D4311yescharacteristic
151C2×C4⋊Q8—862no—
152C2×C4⋊Q8—862no—
153C2×C4⋊Q8C2×D4311yescharacteristic
154C2×C4×Q8—432no—
155C2×C4×Q8—862no—
156#491—22no—
157#487C2×D4314yes—
158#483—862no—
159#475—434no—
160#462—434no—
161#451—862no—
162#441—864no—
163#432—432no—
164#419—22no—
165C4×M16C2×D4311yescharacteristic
166#333—434no—
167Q8⋊C8—438no—
168C43#1855111yescharacteristic, complemented, Sylow
169C22×Q8—432no—
170C22×Q8—862no—
171C22×Q8C22⋊D4312yes—
172C2×Q16—864no—
173C2×M16—21no—
174C4⋊Q8—22no—
175C4⋊Q8—868no—
176C4⋊Q8—868no—
177C4⋊Q8—868no—
178C4⋊Q8—868no—
179C4⋊Q8C22⋊D4312yes—
180C4⋊Q8C22×D4312yes—
181C4⋊Q8C22×D4312yes—
182#125—21no—
183C22⋊Q8—22no—
184C4×Q8—22no—
185C4×Q8—434no—
186C4×Q8—434no—
187C4×Q8—868no—
188C4×Q8—868no—
189C4×Q8—862no—
190C4×Q8—862no—
191#117—21no—
192C2×C4⋊C4—22no—
193C2×C4⋊C4—432no—
194C2×C4⋊C4—864no—
195C2×C4⋊C4—862no—
196C2×C42—862no—
197C2×C42—862no—
198C2×C42C22×D4311yescharacteristic
199#106—864no—
200C4⋊C8—434no—
201#103—28no—
202#103—864no—
203#103—864no—
204C22⋊C8—862no—
205#97—21no—
206#97—862no—
207C4×C8C22×D4312yes—
208C2×Q8—22no—
209C2×Q8—22no—
210C2×Q8—44no—
211C2×Q8—434no—
212C2×Q8—868no—
213C2×Q8—868no—
214C2×Q8—862no—
215C2×Q8—3444no—
216C2×Q8C2×C22⋊D4314yes—
217C22×C4—22no—
218C22×C4—862no—
219C22×C4—862no—
220C22×C4D4×D4312yes—
221C22×C4C2×C22⋊D4311yescharacteristic
222Q16—1728no—
223M16—42no—
224C2×C8—22no—
225C2×C8—864no—
226C4⋊C4—24no—
227C4⋊C4—24no—
228C4⋊C4—22no—
229C4⋊C4—22no—
230C4⋊C4—42no—
231C4⋊C4—434no—
232C4⋊C4—8616no—
233C4⋊C4—862no—
234C4⋊C4—864no—
235C4⋊C4—864no—
236C22⋊C4—41no—
237C42—41no—
238C42—868no—
239C42—864no—
240C42—864no—
241C42D4×D4312yes—
242C42C2×C22⋊D4311yescharacteristic
243C42C23×D4311yescharacteristic
244C23#1306329311yescharacteristic
245Q8—44no—
246Q8—44no—
247Q8—82no—
248Q8—438no—
249Q8—868no—
250Q8—864no—
251Q8—3448no—
252C2×C4—22no—
253C2×C4—24no—
254C2×C4—24no—
255C2×C4—44no—
256C2×C4—42no—
257C2×C4—868no—
258C2×C4—864no—
259C2×C4—864no—
260C2×C4—1724no—
261C2×C4#1306329311yescharacteristic
262C2×C4#1306329312yes—
263C2×C4C2×D4×D4312yes—
264C2×C4C22×C22⋊D4311yescharacteristic
265C8—42no—
266C8—1724no—
267C22—22no—
268C22#1458307612yes—
269C22C2×#1306329311yescharacteristic
270C4—22no—
271C4—21no—
272C4—21no—
273C4—44no—
274C4—82no—
275C4—868no—
276C4—1724no—
277C4#137×D4314yes—
278C2—22no—
279C2#1914382712yes—
280C2C2×#1458307611yescharacteristic
subgroupG/H
centerC22C2×#13063293
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#3139C2
socleC22×C43C2×#120
prime radicalC23×C43#120
hypercenter#3139D43
hypocenterC43#18551
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3139

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
3. #19133813C2semidirect
168. C43#18551semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×#145836292
#191447212
#191338132
#191333212
#191330432
C43×#31392
#1855143